Anand Patel : Counting Hypersurfaces

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

March 28, 2022, 3 p.m.

In

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Abstract

In this talk I will provide an overview of progress (collectively joint with Anand Deopurkar, Mitchell Lee, Hunter Spink, and Dennis Tseng) on a basic problem in enumerative geometry: counting hypersurfaces. In a nutshell, the problem asks to determine universal formulas which count the number of times a particular hypersurface (up to PGL-equivalence) arises in any family. For a prototype: The symmetric Thom-Porteous formula of Harris and Tu, determining the class of the locus where a symmetric map of vector bundles has a particular rank, comprises the "quadric hypersurface case" of the problem. In particular, I will report on the cases of hyperplane arrangements, quartic plane curves, and cubic surfaces.